Spin glass with short-range action in the vicinity of the ''transition''

A model of the quantum (transverse) Ising spin glass with a long-range random interaction is proposed and studied here. In this model the random interaction between two spins at a distance ${r}_{\mathrm{ij}}$ apart falls algebraically as ${1/r}_{\mathrm{ij}}^{(d+\ensuremath{\sigma})/2}.$ Here, apart from the strength of the quantum fluctuations, the interaction range $\ensuremath{\sigma}$ is also tunable. We have studied the ground-state properties of the model, extending the ``Droplet model'' of the short-range quantum spin glass. The model is also studied using a modified form of the effective Landau action describing the transition of the short-range quantum spin glass. The important features which are due to the long-range interaction are clearly mentioned. Field theoretical renormalization group calculations fail to locate any stable weak-coupling fixed point in the non-mean-field region. The simplest conjecture is that beyond the mean-field region, the critical behavior is governed by the infinite randomness fixed point. We extend the phenomenological scaling relation for the short-range quantum spin glass (based on the assumption of the existence of a dangerously irrelevant operator) to the present long-range interacting case. Most of the possible interesting aspects associated with the quantum transition in the present model are elaborately discussed.A model of the quantum (transverse) Ising spin glass with a long-range random interaction is proposed and studied here. In this model the random interaction between two spins at a distance ${r}_{\mathrm{ij}}$ apart falls algebraically as ${1/r}_{\mathrm{ij}}^{(d+\ensuremath{\sigma})/2}.$ Here, apart from the strength of the quantum fluctuations, the interaction range $\ensuremath{\sigma}$ is also tunable. We have studied the ground-state properties of the model, extending the ``Droplet model'' of the short-range quantum spin glass. The model is also studied using a modified form of the effective Landau action describing the transition of the short-range quantum spin glass. The important features which are due to the long-range interaction are clearly mentioned. Field theoretical renormalization group calculations fail to locate any stable weak-coupling fixed point in the non-mean-field region. The simplest conjecture is that beyond the mean-field region, the critical behavior is governed by the infinite randomness fixed point. We extend the phenomenological scaling relation for the short-range quantum spin glass (based on the assumption of the existence of a dangerously irrelevant operator) to the present long-range interacting case. Most of the possible interesting aspects associated with the quantum transition in the present model are elaborately discussed.

Physical review. B, Condensed matterJun 10, 20029 citations

Separation of Time Scales and Reparametrization Invariance for Aging Systems

Claudio Chamon, Malcolm P. Kennett, Horacio E. Castillo +1 more

We show that the generating functional describing the slow dynamics of spin-glass systems is invariant under reparametrizations of the time. This result is general and applies for both infinite and short-range models. It follows simply from the assumption that a separation between short time scales and long time scales exists in the system, and from the constraints of causality and unitarity. Global-time reparametrization invariance suggests that the low action excitations in a spin-glass may be smoothly spatially varying time reparametrizations. These Goldstone modes may provide the basis for an analytic dynamical theory of short-range spin glasses.We show that the generating functional describing the slow dynamics of spin-glass systems is invariant under reparametrizations of the time. This result is general and applies for both infinite and short-range models. It follows simply from the assumption that a separation between short time scales and long time scales exists in the system, and from the constraints of causality and unitarity. Global-time reparametrization invariance suggests that the low action excitations in a spin-glass may be smoothly spatially varying time reparametrizations. These Goldstone modes may provide the basis for an analytic dynamical theory of short-range spin glasses.

arXiv:cond-mat/0109150Physical Review LettersOct 31, 200272 citations

Scaling in a Space of Spin-Glass States

World Scientific lecture notes in physicsJan 1, 19950 citations

Short‐range ±J interaction Ising spin glass in a transverse field on a Bethe lattice: a quantum‐spherical approach

T. K. Kopeć, Klaus D. Usadel

Abstract We consider the short‐range interaction disordered quantum Ising model with symmetric binary ±J bond distribution on the Bethe lattice (with coordination number z). The system exhibits quantum phase transition separating the spin glass and disordered phases where the quantum effect are regulated by a param‐ eter Δ describing the transverse field. By introducing a mapping of the quantum Hamiltonian of the model onto a soft‐spin action we consider it truncated version in a form of the solvable quantized spherical model. Quantum dynamics is examined via various correlation functions on the infinite tree which are evaluated in a closed form. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)Abstract We consider the short‐range interaction disordered quantum Ising model with symmetric binary ±J bond distribution on the Bethe lattice (with coordination number z). The system exhibits quantum phase transition separating the spin glass and disordered phases where the quantum effect are regulated by a param‐ eter Δ describing the transverse field. By introducing a mapping of the quantum Hamiltonian of the model onto a soft‐spin action we consider it truncated version in a form of the solvable quantized spherical model. Quantum dynamics is examined via various correlation functions on the infinite tree which are evaluated in a closed form. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

physica status solidi (b)Dec 8, 200510 citations

A model of the quantum (transverse) Ising spin glass with a long-range random interaction is proposed and studied here. In this model the random interaction between two spins at a distance

{r}_{\mathrm{ij}}

apart falls algebraically as ${1/r}_{\mathrm{ij}}^{(d+\ensuremath{\sigma})/2}.$ Here, apart from the strength of the quantum fluctuations, the interaction range $\ensuremath{\sigma}$ is also tunable. We have studied the ground-state properties of the model, extending the ``Droplet model'' of the short-range quantum spin glass. The model is also studied using a modified form of the effective Landau action describing the transition of the short-range quantum spin glass. The important features which are due to the long-range interaction are clearly mentioned. Field theoretical renormalization group calculations fail to locate any stable weak-coupling fixed point in the non-mean-field region. The simplest conjecture is that beyond the mean-field region, the critical behavior is governed by the infinite randomness fixed point. We extend the phenomenological scaling relation for the short-range quantum spin glass (based on the assumption of the existence of a dangerously irrelevant operator) to the present long-range interacting case. Most of the possible interesting aspects associated with the quantum transition in the present model are elaborately discussed.